# SOCIETY OF ACTUARIES/CASUALTY ACTUARIAL SOCIETY EXAM FM SAMPLE QUESTIONS

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 SOCIETY OF ACTUARIES/CASUALTY ACTUARIAL SOCIETY EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS Copyright 2005 by the Society of Actuaries and the Casualty Actuarial Society Some of the questions in this study note are taken from past SOA/CAS examinations. FM PRINTED IN U.S.A. 11/08/04 2

2 These questions are representative of the types of questions that might be asked of candidates sitting for the new examination on Financial Mathematics (2/FM). These questions are intended to represent the depth of understanding required of candidates. The distribution of questions by topic is not intended to represent the distribution of questions on future exams. 11/08/04 3

3 1. Bruce deposits 100 into a bank account. His account is credited interest at a nominal rate of interest of 4% convertible semiannually. At the same time, Peter deposits 100 into a separate account. Peter s account is credited interest at a force of interest of δ. After 7.25 years, the value of each account is the same. Calculate δ. (A) (B) (C) (D) (E) /08/04 4

4 2. Kathryn deposits 100 into an account at the beginning of each 4-year period for 40 years. The account credits interest at an annual effective interest rate of i. The accumulated amount in the account at the end of 40 years is X, which is 5 times the accumulated amount in the account at the end of 20 years. Calculate X. (A) 4695 (B) 5070 (C) 5445 (D) 5820 (E) /08/04 5

5 3. Eric deposits 100 into a savings account at time 0, which pays interest at a nominal rate of i, compounded semiannually. Mike deposits 200 into a different savings account at time 0, which pays simple interest at an annual rate of i. Eric and Mike earn the same amount of interest during the last 6 months of the 8 th year. Calculate i. (A) 9.06% (B) 9.26% (C) 9.46% (D) 9.66% (E) 9.86% 11/08/04 6

6 4. John borrows 10,000 for 10 years at an annual effective interest rate of 10%. He can repay this loan using the amortization method with payments of 1, at the end of each year. Instead, John repays the 10,000 using a sinking fund that pays an annual effective interest rate of 14%. The deposits to the sinking fund are equal to 1, minus the interest on the loan and are made at the end of each year for 10 years. Determine the balance in the sinking fund immediately after repayment of the loan. (A) 2,130 (B) 2,180 (C) 2,230 (D) 2,300 (E) 2,370 11/08/04 7

7 5. An association had a fund balance of 75 on January 1 and 60 on December 31. At the end of every month during the year, the association deposited 10 from membership fees. There were withdrawals of 5 on February 28, 25 on June 30, 80 on October 15, and 35 on October 31. Calculate the dollar-weighted (money-weighted) rate of return for the year. (A) 9.0% (B) 9.5% (C) 10.0% (D) 10.5% (E) 11.0% 11/08/04 8

8 6. A perpetuity costs 77.1 and makes annual payments at the end of the year. The perpetuity pays 1 at the end of year 2, 2 at the end of year 3,., n at the end of year (n+1). After year (n+1), the payments remain constant at n. The annual effective interest rate is 10.5%. Calculate n. (A) 17 (B) 18 (C) 19 (D) 20 (E) 21 11/08/04 9

9 is deposited into Fund X, which earns an annual effective rate of 6%. At the end of each year, the interest earned plus an additional 100 is withdrawn from the fund. At the end of the tenth year, the fund is depleted. The annual withdrawals of interest and principal are deposited into Fund Y, which earns an annual effective rate of 9%. Determine the accumulated value of Fund Y at the end of year 10. (A) 1519 (B) 1819 (C) 2085 (D) 2273 (E) /08/04 10

10 8. You are given the following table of interest rates: Calendar Year of Original Investment Investment Year Rates (in %) i 1 y i 2 y i 3 y i 4 y i 5 y Portfolio Rates (in %) i y+5 y A person deposits 1000 on January 1, Let the following be the accumulated value of the 1000 on January 1, 2000: P: under the investment year method Q: under the portfolio yield method R: where the balance is withdrawn at the end of every year and is reinvested at the new money rate Determine the ranking of P, Q, and R. (A) P> Q> R (B) P> R> Q (C) Q> P> R (D) R > P> Q (E) R > Q> P 11/08/04 11

11 9. A 20-year loan of 1000 is repaid with payments at the end of each year. Each of the first ten payments equals 150% of the amount of interest due. Each of the last ten payments is X. The lender charges interest at an annual effective rate of 10%. Calculate X. (A) 32 (B) 57 (C) 70 (D) 97 (E) /08/04 12

12 10. A 10,000 par value 10-year bond with 8% annual coupons is bought at a premium to yield an annual effective rate of 6%. Calculate the interest portion of the 7 th coupon. (A) 632 (B) 642 (C) 651 (D) 660 (E) /08/04 13

13 11. A perpetuity-immediate pays 100 per year. Immediately after the fifth payment, the perpetuity is exchanged for a 25-year annuity-immediate that will pay X at the end of the first year. Each subsequent annual payment will be 8% greater than the preceding payment. The annual effective rate of interest is 8%. Calculate X. (A) 54 (B) 64 (C) 74 (D) 84 (E) 94 11/08/04 14

14 12. Jeff deposits 10 into a fund today and 20 fifteen years later. Interest is credited at a nominal discount rate of d compounded quarterly for the first 10 years, and at a nominal interest rate of 6% compounded semiannually thereafter. The accumulated balance in the fund at the end of 30 years is 100. Calculate d. (A) 4.33% (B) 4.43% (C) 4.53% (D) 4.63% (E) 4.73% 11/08/04 15

15 13. Ernie makes deposits of 100 at time 0, and X at time 3. The fund grows at a force of interest 2 t δ t =, t > The amount of interest earned from time 3 to time 6 is also X. Calculate X. (A) 385 (B) 485 (C) 585 (D) 685 (E) /08/04 16

16 14. Mike buys a perpetuity-immediate with varying annual payments. During the first 5 years, the payment is constant and equal to 10. Beginning in year 6, the payments start to increase. For year 6 and all future years, the current year s payment is K% larger than the previous year s payment. At an annual effective interest rate of 9.2%, the perpetuity has a present value of Calculate K, given K < 9.2. (A) 4.0 (B) 4.2 (C) 4.4 (D) 4.6 (E) /08/04 17

17 15. A 10-year loan of 2000 is to be repaid with payments at the end of each year. It can be repaid under the following two options: (i) Equal annual payments at an annual effective rate of 8.07%. (ii) Installments of 200 each year plus interest on the unpaid balance at an annual effective rate of i. The sum of the payments under option (i) equals the sum of the payments under option (ii). Determine i. (A) 8.75% (B) 9.00% (C) 9.25% (D) 9.50% (E) 9.75% 11/08/04 18

18 16. A loan is amortized over five years with monthly payments at a nominal interest rate of 9% compounded monthly. The first payment is 1000 and is to be paid one month from the date of the loan. Each succeeding monthly payment will be 2% lower than the prior payment. Calculate the outstanding loan balance immediately after the 40 th payment is made. (A) 6751 (B) 6889 (C) 6941 (D) 7030 (E) /08/04 19

19 17. To accumulate 8000 at the end of 3n years, deposits of 98 are made at the end of each of the first n years and 196 at the end of each of the next 2n years. The annual effective rate of interest is i. You are given (l + i) n = 2.0. Determine i. (A) 11.25% (B) 11.75% (C) 12.25% (D) 12.75% (E) 13.25% 11/08/04 20

20 18. Olga buys a 5-year increasing annuity for X. Olga will receive 2 at the end of the first month, 4 at the end of the second month, and for each month thereafter the payment increases by 2. The nominal interest rate is 9% convertible quarterly. Calculate X. (A) 2680 (B) 2730 (C) 2780 (D) 2830 (E) /08/04 21

21 19. You are given the following information about the activity in two different investment accounts: Account K Fund value Activity Date before activity Deposit Withdrawal January 1, July 1, X October 1, X December 31, Account L Fund value Activity Date before activity Deposit Withdrawal January 1, July 1, X December 31, During 1999, the dollar-weighted (money-weighted) return for investment account K equals the time-weighted return for investment account L, which equals i. Calculate i. (A) 10% (B) 12% (C) 15% (D) 18% (E) 20% 11/08/04 22

22 20. David can receive one of the following two payment streams: (i) 100 at time 0, 200 at time n, and 300 at time 2n (ii) 600 at time 10 At an annual effective interest rate of i, the present values of the two streams are equal. Given v n = 0.76, determine i. (A) 3.5% (B) 4.0% (C) 4.5% (D) 5.0% (E) 5.5% 11/08/04 23

23 21. Payments are made to an account at a continuous rate of (8k + tk), where 0 t 10. Interest is credited at a force of interest δ t = t. After 10 years, the account is worth 20,000. Calculate k. (A) 111 (B) 116 (C) 121 (D) 126 (E) /08/04 24

24 22. You have decided to invest in Bond X, an n-year bond with semi-annual coupons and the following characteristics: Par value is The ratio of the semi-annual coupon rate to the desired semi-annual yield rate, r i, is The present value of the redemption value is Given v n = , what is the price of bond X? (A) 1019 (B) 1029 (C) 1050 (D) 1055 (E) /08/04 25

25 23. Project P requires an investment of 4000 at time 0. The investment pays 2000 at time 1 and 4000 at time 2. Project Q requires an investment of X at time 2. The investment pays 2000 at time 0 and 4000 at time 1. The net present values of the two projects are equal at an interest rate of 10%. Calculate X. (A) 5400 (B) 5420 (C) 5440 (D) 5460 (E) /08/04 26

26 24. A 20-year loan of 20,000 may be repaid under the following two methods: i) amortization method with equal annual payments at an annual effective rate of 6.5% ii) sinking fund method in which the lender receives an annual effective rate of 8% and the sinking fund earns an annual effective rate of j Both methods require a payment of X to be made at the end of each year for 20 years. Calculate j. (A) j 6.5% (B) 6.5% < j 8.0% (C) 8.0% < j 10.0% (D) 10.0% < j 12.0% (E) j > 12.0% 11/08/04 27

27 25. A perpetuity-immediate pays X per year. Brian receives the first n payments, Colleen receives the next n payments, and Jeff receives the remaining payments. Brian's share of the present value of the original perpetuity is 40%, and Jeff's share is K. Calculate K. (A) 24% (B) 28% (C) 32% (D) 36% (E) 40% 11/08/04 28

28 26. Seth, Janice, and Lori each borrow 5000 for five years at a nominal interest rate of 12%, compounded semi-annually. Seth has interest accumulated over the five years and pays all the interest and principal in a lump sum at the end of five years. Janice pays interest at the end of every six-month period as it accrues and the principal at the end of five years. Lori repays her loan with 10 level payments at the end of every six-month period. Calculate the total amount of interest paid on all three loans. (A) 8718 (B) 8728 (C) 8738 (D) 8748 (E) /08/04 29

29 27. Bruce and Robbie each open up new bank accounts at time 0. Bruce deposits 100 into his bank account, and Robbie deposits 50 into his. Each account earns the same annual effective interest rate. The amount of interest earned in Bruce's account during the 11th year is equal to X. The amount of interest earned in Robbie's account during the 17th year is also equal to X. Calculate X. (A) 28.0 (B) 31.3 (C) 34.6 (D) 36.7 (E) /08/04 30

30 28. Ron is repaying a loan with payments of 1 at the end of each year for n years. The amount of interest paid in period t plus the amount of principal repaid in period t + 1 equals X. Calculate X. (A) 1 + v i n t (B) 1 + v d n t (C) 1 + v n t i (D) (E) 1 + v n t d 1 + v n t 11/08/04 31

31 29. At an annual effective interest rate of i, i > 0%, the present value of a perpetuity paying `10 at the end of each 3-year period, with the first payment at the end of year 3, is 32. At the same annual effective rate of i, the present value of a perpetuity paying 1 at the end of each 4-month period, with first payment at the end of 4 months, is X. Calculate X. (A) 31.6 (B) 32.6 (C) 33.6 (D) 34.6 (E) /08/04 32

32 30. As of 12/31/03, an insurance company has a known obligation to pay \$1,000,000 on 12/31/2007. To fund this liability, the company immediately purchases 4-year 5% annual coupon bonds totaling \$822,703 of par value. The company anticipates reinvestment interest rates to remain constant at 5% through 12/31/07. The maturity value of the bond equals the par value. Under the following reinvestment interest rate movement scenarios effective 1/1/2004, what best describes the insurance company s profit or (loss) as of 12/31/2007 after the liability is paid? Interest Rates Drop Interest Rates Increase by ½% by ½% (A) +6, ,147 (B) (14,757) +14,418 (C) (18,911) +19,185 (D) (1,313) +1,323 (E) Breakeven Breakeven 11/08/04 33

33 31. An insurance company has an obligation to pay the medical costs for a claimant. Average annual claims costs today are \$5,000, and medical inflation is expected to be 7% per year. The claimant is expected to live an additional 20 years. Claim payments are made at yearly intervals, with the first claim payment to be made one year from today. Find the present value of the obligation if the annual interest rate is 5%. (A) 87,932 (B) 102,514 (C) 114,611 (D) 122,634 (E) Cannot be determined 11/08/04 34

34 32. An investor pays \$100,000 today for a 4-year investment that returns cash flows of \$60,000 at the end of each of years 3 and 4. The cash flows can be reinvested at 4.0% per annum effective. If the rate of interest at which the investment is to be valued is 5.0%, what is the net present value of this investment today? (A) (B) -699 (C) 699 (D) 1398 (E) 2,629 11/08/04 35

35 33. You are given the following information with respect to a bond: par amount: 1000 term to maturity 3 years annual coupon rate 6% payable annually Term Annual Spot Interest Rates 1 7% 2 8% 3 9% Calculate the value of the bond. (A) 906 (B) 926 (C) 930 (D) 950 (E) /08/04 36

36 34. You are given the following information with respect to a bond: par amount: 1000 term to maturity 3 years annual coupon rate 6% payable annually Term Annual Spot Interest Rates 1 7% 2 8% 3 9% Calculate the annual effective yield rate for the bond if the bond is sold at a price equal to its value. (A) 8.1% (B) 8.3% (C) 8.5% (D) 8.7% (E) 8.9% 11/08/04 37

37 35. The current price of an annual coupon bond is 100. The derivative of the price of the bond with respect to the yield to maturity is The yield to maturity is an annual effective rate of 8%. Calculate the duration of the bond. (A) 7.00 (B) 7.49 (C) 7.56 (D) 7.69 (E) /08/04 38

38 36. Calculate the duration of a common stock that pays dividends at the end of each year into perpetuity. Assume that the dividend is constant, and that the effective rate of interest is 10%. (A) 7 (B) 9 (C) 11 (D) 19 (E) 27 11/08/04 39

39 37. Calculate the duration of a common stock that pays dividends at the end of each year into perpetuity. Assume that the dividend increases by 2% each year and that the effective rate of interest is 5%. (A) 27 (B) 35 (C) 44 (D) 52 (E) 58 11/08/04 40

40 38. Eric and Jason each sell a different stock short at the beginning of the year for a price of 800. The margin requirement for each investor is 50% and each will earn an annual effective interest rate of 8% on his margin account. Each stock pays a dividend of 16 at the end of the year. Immediately thereafter, Eric buys back his stock at a price of (800-2X), and Jason buys back his stock at a price of (800 + X). Eric s annual effective yield, i, on the short sale is twice Jason s annual effective yield. Calculate i. (A) 4% (B) 6% (C) 8% (D) 10% (E) 12% 11/08/04 41

41 39. Jose and Chris each sell a different stock short for the same price. For each investor, the margin requirement is 50% and interest on the margin debt is paid at an annual effective rate of 6%. Each investor buys back his stock one year later at a price of 760. Jose s stock paid a dividend of 32 at the end of the year while Chris s stock paid no dividends. During the 1-year period, Chris s return on the short sale is i, which is twice the return earned by Jose. Calculate i. (A) 12% (B) 16% (C) 18% (D) 20% (E) 24% 11/08/04 42

42 40. Bill and Jane each sell a different stock short for a price of For both investors, the margin requirement is 50%, and interest on the margin is credited at an annual effective rate of 6%. Bill buys back his stock one year later at a price of P. At the end of the year, the stock paid a dividend of X. Jane also buys back her stock after one year, at a price of (P 25). At the end of the year, her stock paid a dividend of 2X. Both investors earned an annual effective yield of 21% on their short sales. Calculate P. (A) 800 (B) 825 (C) 850 (D) 875 (E) /08/04 43

43 41. * On January 1, 2005, Marc has the following options for repaying a loan: Sixty monthly payments of 100 beginning February 1, A single payment of 6000 at the end of K months. Interest is at a nominal annual rate of 12% compounded monthly. The two options have the same present value. Determine K. (A) 29.0 (B) 29.5 (C) 30.0 (D) 30.5 (E) 31.0 *Reprinted with permission from ACTEX Publications 11/08/04 44

44 42. * You are given an annuity-immediate with 11 annual payments of 100 and a final payment at the end of 12 years. At an annual effective interest rate of 3.5%, the present value at time 0 of all payments is Calculate the final payment. (A) 146 (B) 151 (C) 156 (D) 161 (E) 166 * Reprinted with permission from ACTEX Publications. 11/08/04 45

45 43. * A 10,000 par value bond with coupons at 8%, convertible semiannually, is being sold 3 years and 4 months before the bond matures. The purchase will yield 6% convertible semiannually to the buyer. The price at the most recent coupon date, immediately after the coupon payment, was Calculate the market price of the bond, assuming compound interest throughout. (A) 5500 (B) 5520 (C) 5540 (D) 5560 (E) 5580 * Reprinted with permission from ACTEX Publications. 11/08/04 46

46 44. * A 1000 par value 10-year bond with coupons at 5%, convertible semiannually, is selling for Calculate the yield rate convertible semiannually. (A) 1.00% (B) 2.00% (C) 3.00% (D) 4.00% (E) 5.00% * Reprinted with permission from ACTEX Publications. 11/08/04 47

47 45. You are given the following information about an investment account: Date Value Immediately Before Deposit Deposit January 1 10 July 1 12 X December X 31 Over the year, the time-weighted return is 0%, and the dollar-weighted (moneyweighted) return is Y. Calculate Y. (A) -25% (B) -10% (C) 0% (D) 10% (E) 25% 11/08/04 48

48 46. Seth borrows X for four years at an annual effective interest rate of 8%, to be repaid with equal payments at the end of each year. The outstanding loan balance at the end of the third year is Calculate the principal repaid in the first payment. (A) 444 (B) 454 (C) 464 (D) 474 (E) /08/04 49

49 47. Bill buys a 10-year 1000 par value 6% bond with semi-annual coupons. The price assumes a nominal yield of 6%, compounded semi-annually. As Bill receives each coupon payment, he immediately puts the money into an account earning interest at an annual effective rate of i. At the end of 10 years, immediately after Bill receives the final coupon payment and the redemption value of the bond, Bill has earned an annual effective yield of 7% on his investment in the bond. Calculate i. (A) 9.50% (B) 9.75% (C) 10.00% (D) 10.25% (E) 10.50% 11/08/04 50

50 48. A man turns 40 today and wishes to provide supplemental retirement income of 3000 at the beginning of each month starting on his 65th birthday. Starting today, he makes monthly contributions of X to a fund for 25 years. The fund earns a nominal rate of 8% compounded monthly. On his 65 th birthday, each 1000 of the fund will provide 9.65 of income at the beginning of each month starting immediately and continuing as long as he survives. Calculate X. (A) (B) (C) (D) (E) /08/04 51

51 49. Happy and financially astute parents decide at the birth of their daughter that they will need to provide 50,000 at each of their daughter s 18 th, 19 th, 20 th and 21 st birthdays to fund her college education. They plan to contribute X at each of their daughter s 1 st through 17 th birthdays to fund the four 50,000 withdrawals. If they anticipate earning a constant 5% annual effective rate on their contributions, which the following equations of value can be used to determine X, assuming compound interest? (A) X [ v + v +... v ] = 50,000[ v +... ] v (B) X [(1.05) + (1.05) +...(1.05) ] = 50,000[ v ] (C) X [(1.05) + (1.05) +...1] = 50,000[ v ] (D) X [(1.05) + (1.05) +...(1.05) ] = 50,000[ v ] (E) X [(1 + v +... v ] = 50,000[ v +... ] v.05 11/08/04 52

52 50. A 1000 bond with semi-annual coupons at i (2) = 6% matures at par on October 15, The bond is purchased on June 28, 2005 to yield the investor i (2) = 7%. What is the purchase price? Assume simple interest between bond coupon dates and note that: Date Day of the Year April June October (A) 906 (B) 907 (C) 908 (D) 919 (E) /08/04 53

53 The following information applies to questions 51 thru 53. Joe must pay liabilities of 1,000 due 6 months from now and another 1,000 due one year from now. There are two available investments: a 6-month bond with face amount of 1,000, a 8% nominal annual coupon rate convertible semiannually, and a 6% nominal annual yield rate convertible semiannually; and a one-year bond with face amount of 1,000, a 5% nominal annual coupon rate convertible semiannually, and a 7% nominal annual yield rate convertible semiannually 51. How much of each bond should Joe purchase in order to exactly (absolutely) match the liabilities? Bond I Bond II (A) (B) (C) (D) (E) /08/04 54

54 The following information applies to questions 51 thru 53. Joe must pay liabilities of 1,000 due 6 months from now and another 1,000 due one year from now. There are two available investments: a 6-month bond with face amount of 1,000, a 8% nominal annual coupon rate convertible semiannually, and a 6% nominal annual yield rate convertible semiannually; and a one-year bond with face amount of 1,000, a 5% nominal annual coupon rate convertible semiannually, and a 7% nominal annual yield rate convertible semiannually 52. What is Joe s total cost of purchasing the bonds required to exactly (absolutely) match the liabilities? (A) 1894 (B) 1904 (C) 1914 (D) 1924 (E) /08/04 55

55 The following information applies to questions 51 thru 53. Joe must pay liabilities of 1,000 due 6 months from now and another 1,000 due one year from now. There are two available investments: a 6-month bond with face amount of 1,000, a 8% nominal annual coupon rate convertible semiannually, and a 6% nominal annual yield rate convertible semiannually; and a one-year bond with face amount of 1,000, a 5% nominal annual coupon rate convertible semiannually, and a 7% nominal annual yield rate convertible semiannually 53. What is the annual effective yield rate for investment in the bonds required to exactly (absolutely) match the liabilities? (A) 6.5% (B) 6.6% (C) 6.7% (D) 6.8% (E) 6.9% 11/08/04 56

56 54. Matt purchased a 20-year par value bond with semiannual coupons at a nominal annual rate of 8% convertible semiannually at a price of The bond can be called at par value X on any coupon date starting at the end of year 15 after the coupon is paid. The price guarantees that Matt will receive a nominal annual rate of interest convertible semiannually of at least 6%. Calculate X. (A) 1400 (B) 1420 (C) 1440 (D) 1460 (E) /08/04 57

57 55. Toby purchased a 20-year par value bond with semiannual coupons at a nominal annual rate of 8% convertible semiannually at a price of The bond can be called at par value 1100 on any coupon date starting at the end of year 15. What is the minimum yield that Toby could receive, expressed as a nominal annual rate of interest convertible semiannually? (A) 3.2% (B) 3.3% (C) 3.4% (D) 3.5% (E) 3.6% 11/08/04 58

58 56. Sue purchased a 10-year par value bond with semiannual coupons at a nominal annual rate of 4% convertible semiannually at a price of The bond can be called at par value X on any coupon date starting at the end of year 5. The price guarantees that Sue will receive a nominal annual rate of interest convertible semiannually of at least 6%. Calculate X. (A) 1120 (B) 1140 (C) 1160 (D) 1180 (E) /08/04 59

59 57. Mary purchased a 10-year par value bond with semiannual coupons at a nominal annual rate of 4% convertible semiannually at a price of The bond can be called at par value 1100 on any coupon date starting at the end of year 5. What is the minimum yield that Mary could receive, expressed as a nominal annual rate of interest convertible semiannually? (A) 4.8% (B) 4.9% (C) 5.0% (D) 5.1% (E) 5.2% 11/08/04 60

60 EXAM 2/FM SAMPLE QUESTIONS SOLUTIONS SOCIETY OF ACTUARIES/CASUALTY ACTUARIAL SOCIETY EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE SOLUTIONS Copyright 2005 by the Society of Actuaries and the Casualty Actuarial Society Some of the questions in this study note are taken from past SOA/CAS examinations. FM PRINTED IN U.S.A. 11/03/04 1

61 EXAM 2/FM SAMPLE QUESTIONS SOLUTIONS The following model solutions are presented for educational purposes. Alternate methods of solution are, of course, acceptable. 1. Solution: C Given the same principal invested for the same period of time yields the same accumulated value, the two (2) i measures of interest i (2) 2 δ and δ must be equivalent, which means: ( 1+ ) = e over one interest 2 measurement period (a year in this case). Thus, δ ( 1+ ) = e or Solution: E 2 δ ( 1+.02) = e and = ln(1.02) 2 = 2ln(1.02) = δ or 3.96%. Accumulated value end of 40 years = 100 [(1+i) 4 + (1+i) 8 +..(1+i) 40 ]= 100 ((1+i) 4 )[1-((1+i) 4 ) 10 ]/[1 - (1+i) 4 ] ( Sum of finite geometric progression = 1 st term times [1 (common ratio) raised to the number of terms] divided by [1 common ratio] ) and accumulated value end of 20 years = 100 [(1+i) 4 + (1+i) 8 +..(1+i) 20 ]=100 ((1+i) 4 )[1-((1+i) 4 ) 5 ]/[1 - (1+i) 4 ] But accumulated value end of 40 years = 5 times accumulated value end of 20 years Thus, 100 ((1+i) 4 )[1-((1+i) 4 ) 10 ]/[1 - (1+i) 4 ] = 5 {100 ((1+i) 4 )[1-((1+i) 4 ) 5 ]/[1 - (1+i) 4 ]} Or, for i > 0, 1-((1+i) 40 = 5 [1-((1+i) 20 ] or [1-((1+i) 40 ]/[1-((1+i) 20 ] = 5 But x 2 - y 2 = [x-y] [x+y], so [1-((1+i) 40 ]/[1-((1+i) 20 ]= [1+((1+i) 20 ] Thus, [1+((1+i) 20 ] = 5 or (1+i) 20 = 4. So X = Accumulated value at end of 40 years = 100 ((1+i) 4 )[1-((1+i) 4 ) 10 ]/[1 - (1+i) 4 ] =100 (4 1/5 )[1-((4 1/5 ) 10 ]/[1 4 1/5 ] = Alternate solution using annuity symbols: End of year 40, accumulated value = 100 ( s / a ), and end of year accumulated value = 100 ( s / a ). Given the ratio of the values equals 5, then = ( s / s ) = [(1 + i) 1]/[(1 + i) 1] = [(1 + i) 1]. Thus, (1+i) 20 = 4 and the accumulated value at the end of 40 years is 100( s / a ) = 100[(1 + i) 1]/[1 (1 + i) ] = 100[16 1]/[1 4 1/ ] = /03/04 2

62 EXAM 2/FM SAMPLE QUESTIONS SOLUTIONS Note: if i = 0 the conditions of the question are not satisfied because then the accumulated value at the end of 40 years = 40 (100) = 4000, and the accumulated value at the end of 20 years = 20 (100) = 2000 and thus accumulated value at the end of 40 years is not 5 times the accumulated value at the end of 20 years. 11/03/04 3

63 EXAM 2/FM SAMPLE QUESTIONS SOLUTIONS 3. Solution: C i Eric s interest (compound interest), last 6 months of the 8 th 15 i year: 100(1 + ) ( ) 2 2 Mike s interest (simple interest), last 6 months of the 8 th year: 200( i i 15 i i ). Thus, 100(1 + ) ( ) = 200( ) or (1 + i ) 15 = 2, which means i/2 = or 2 i = = 9.46% Solution: A The payment using the amortization method is The periodic interest is.10(10000) = Thus, deposits into the sinking fund are = Then, the amount in sinking fund at end of 10 years is Using BA II Plus calculator keystrokes: 2 nd FV (to clear registers) 10 N, 14 I/Y, PMT, CPT FV +/ = yields (Using BA 35 Solar keystrokes are AC/ON (to clear registers) 10 N 14 %i PMT CPT FV +/ =) Solution: E Key formulas for estimating dollar-weighted rate of return: Fund January 1 + deposits during year withdrawals during year + interest = Fund December 31. Estimate of dollar weighted rate of return = amount of interest divided by the weighted average amount of fund exposed to earning interest total deposits = 120 total withdrawals = 145 Investment income = = Rate of return = = 10/ = 11% s /03/04 4

64 EXAM 2/FM SAMPLE QUESTIONS SOLUTIONS 6. Solution: C nv = + n i Cost of the perpetuity v ( Ia) = v + i a nv nv i i i an = i n n+ 1 a nv n nv n+ 1 n+ 1 n = + Given i = 10.5%, a i n i n+ 1 an = = a = , at 10.5% n n = 19 Tips: Helpful analysis tools for varying annuities: draw picture, identify layers of level payments, and add values of level layers. In this question, first layer gives a value of 1/i (=PV of level perpetuity of 1 = sum of an infinite geometric progression with common ratio v, which reduces to 1/i) at 1, or v (1/i) at 0 2 nd layer gives a value of 1/i at 2, or v 2 (1/i) at 0. n th layer gives a value of 1/i at n, or v n (1/i) at 0 Thus 77.1 = PV = (1/i) (v + v 2 +. v n ) = (1/.105) a n. 105 n can be easily solved for using BA II Plus or BA 35 Solar calculator 11/03/04 5

65 EXAM 2/FM SAMPLE QUESTIONS SOLUTIONS 7. Solution: C ( Ds) s ( 1.09) s ( ) Helpful general result for obtaining PV or Accumulated Value (AV) of arithmetically varying sequence of payments with interest conversion period (ICP) equal to payment period (PP): Given: Initial payment P at end of 1 st PP; increase per PP = Q (could be negative); number of payments = n; effective rate per PP = i (in decimal form). Then PV = P a n i. + Q [( a n i. n v n )/i] (if first payment is at beginning of first PP, just multiply this result by (1+i)) To efficiently use special calculator keys, simplify to: (P + Q/i) a n i. n Q v n / i = (P + Q/i) a n i. n (Q/i) v n. Then for BA II Plus: select 2 nd FV, enter value of n select N, enter value of 100i select I/Y, enter value of (P+(Q/i)) select PMT, enter value of ( n (Q/i)) select FV, CPT PV +/- For accumulated value: select 2 nd FV, enter value of n select N, enter value of 100i select I/Y, enter value of (P+(Q/i)), select PMT, CPT FV select +/- select enter value of (n (Q/i)) = For this question: Initial payment into Fund Y is 160, increase per PP = - 6 BA II Plus: 2 nd FV, 10 N, 9 I/Y, (160 (6/.09)) PMT, CPT FV +/- + (60/.09) = yields (For BA 35 Solar: AC/ON, 10 N, 9 %i, (6/.09 = +/ =) PMT, CPT FV +/- STO, 60/.09 + RCL (MEM) =) Solution: D ( )( )( ) ( )( )( ) ( )( )( ) P = = Q = = R = = Thus, R > P> Q. 11/03/04 6

66 EXAM 2/FM SAMPLE QUESTIONS SOLUTIONS 9. Solution: D For the first 10 years, each payment equals 150% of interest due. The lender charges 10%, therefore 5% of the principal outstanding will be used to reduce the principal. At the end of 10 years, the amount outstanding is ( ) = Thus, the equation of value for the last 10 years using a comparison date of the end of year 10 is = X a. So X = 10 10% = a 10 10% Alternatively, derive answer from basic principles rather than intuition. Equation of value at time 0: 1000 = 1.5 (1000 (v +.95 v v v 10 ) + X v 10 a Thus X = [ {1.5 (1000 (v +.95 v v v 10 )}]/ (v 10 a ) = {1000 [150 v (1 (.95 v) 10 )/(1-.95 v)]}/ (v 10 a )= Solution: B i = 6% 4 BV = 10, 000v + 800a = = 10, I = i BV = , 693 = Solution: A Value of initial perpetuity immediately after the 5 th payment (or any other time) = 100 (1/i) = 100/.08 = Exchange for 25-year annuity-immediate paying X at the end of the first year, with each subsequent payment increasing by 8%, implies 1250 (value of the perpetuity) must = X (v v v v 25 ) (value of 25-year annuity-immediate) = X ( (1.08) (1.08) (1.08) -25 ) (because the annual effective rate of interest is 8%) = X ( ) = X [25( )]. So, 1250 (1.08) = 25 X or X = 54 11/03/04 7

67 EXAM 2/FM SAMPLE QUESTIONS SOLUTIONS 12. Solution: C Equation of value at end of 30 years: 40 ( d 4) ( ) ( ) 40 10( 1 d ) = = Solution: E 4 1 d = d = t t dt = So accumulated value at time 3 of deposit of 100 at time 0 is: t 3 / e = The amount of interest earned from time 3 to time 6 equals the accumulated value at time 6 minus the accumulated value at time 3. Thus 3 t /300 3 ( ) ( ) 6 + X e + X = X ( )( ) X X = X = X X = Solution: A = Present value = 10a + 10v t= (1 + k) [ t ] k 1 = v ( ) because the summation is an infinite geometric progression, which simplifies k to (1/(1-common ratio)) as long as the absolute value of the common ratio is less than 1 (i.e. in this case common ratio is (1+k)/1.092 and so k must be less than.092) ( )( ) So = k ( or = 6.44)( 1 + k ) or 20 = (1+k)/(0.092-k) k k and thus 0.84 = 21 k or k = Answer is /03/04 8

68 EXAM 2/FM SAMPLE QUESTIONS SOLUTIONS 15. Solution: B Option 1: 2000 = Pa P = 299 Total payments = 2990 Option 2: Interest needs to be = i[ ] = i [ 11, 000] i = 0.09 Tip: For an arithmetic progression, the sum equals the average of the first and last terms times the number of terms. Thus in this case, = (1/2) ( ) 10 = Of course, with only 10 terms, it s fairly quick to just add them on the calculator! Solution: B The point of this question is to test whether a student can determine the outstanding balance of a loan when the payments are not level. Monthly payment at time t = 1000(0.98) t 1 Since the actual amount of the loan is not given, the outstanding balance must be calculated prospectively, OB 40 = present value of payments at time 41 to time 60 = 1000(0.98) 40 (1.0075) (0.98) 41 (1.0075) (0.98) 59 (1.0075) 20 This is the sum of a finite geometric series, with first term, a = 1000(0.98) 40 (1.0075) 1 common ratio, r = (0.98)(1.0075) 1 number of terms, n = 20 Thus, the sum = a (1 r n )/(1 r) = 1000(0.98) 40 (1.0075) 1 [1 (0.98/1.0075) 20 ]/[1 (0.98/1.0075)] = /03/04 9

69 EXAM 2/FM SAMPLE QUESTIONS SOLUTIONS 17. Solution: C The payments can be separated into two layers of 98 and the equation of value at 3n is 98 S + 98S = n 2n 3n 2n (1 + i) 1 (1 + i) 1 + = i i n ( 1+ i) = = i i 10 = i i = 12.25% Solution: B Convert 9% convertible quarterly to an effective rate per month, the payment period. That is, solve for j such 3.09 that (1 + j ) = (1 + ) or j = or.744% 4 Then.. 60 a v 2( Ia ) = 2[ ] = Alternatively, use result listed in solution to question 7 above with P = Q = 2, i = and n = 60. Then (P + Q/i) = (2 + 2/.00744) = and n Q/i = Using BA II Plus calculator: select 2 nd FV, enter 60 select N, enter.744 select I/Y, enter select PMT, enter select FV, CPT PV +/- yields /03/04 10

70 EXAM 2/FM SAMPLE QUESTIONS SOLUTIONS 19. Solution: C Key formulas for estimating dollar-weighted rate of return: Fund January 1 + deposits during year withdrawals during year + interest = Fund December 31. Estimate of dollar weighted rate of return = amount of interest divided by the weighted average amount of fund exposed to earning interest Then for Account K, dollar-weighted return: Amount of interest I = x + x = 25 x 25 x i = = (25 x)/100; or (1 + i) K = (125 x)/ x + 2x 2 4 Key concepts for time-weighted rate of return: Divide the time period into subintervals for each time there is a deposit or withdrawal For each subinterval, calculate the ratio of the amount in the fund at the end of the subinterval (before the deposit or withdrawal at the end of the subinterval) to the amount in the fund at the beginning of the subinterval (after the deposit or withdrawal) Multiply the ratios together to cover the desired time period Then for Account L time-weighted return: (1 + i) = 125/ /(125 x) = /(125 x) But (1 + i) = (1 + i) for Account K. So /(125 x) = (125 x)/100 or (125 x) 2 = 13,225 x = 10 and i = (25 x)/100 = 15% Solution: A Equate present values: v n v 2n = 600 v 10 v n = = Thus, v 10 = /600 = i = 3.5% Solution: A Use equation of value at end of 10 years: ( 1 ) 10 1 dt n 8+ t n ln( 8+ t) n + i = e = e = 18 ( 8 + n) t , 000 = ( 8k + t k ) ( 1+ i) dt = ( 8 ) 0 k + t dt t 10 20, 000 = 18k t 0 = 180k k = = /03/04 11

71 EXAM 2/FM SAMPLE QUESTIONS SOLUTIONS /03/04 12

72 EXAM 2/FM SAMPLE QUESTIONS SOLUTIONS 22. Solution: D Price for any bond is the present value at the yield rate of the coupons plus the present value at the yield rate of the redemption value. Given r = semi-annual coupon rate and i = the semi-annual yield rate. Let C = redemption value. Then Price for bond X = P X = 1000 r a 2 ni + C v 2n (using a semi-annual yield rate throughout) = 1000 i r (1 v 2n ) because given as a 2 ni = 1 v 2n i and the present value of the redemption value, C v 2n, is We are also given i r = so 1000 i r = Thus, P X = (1 v 2n ) Now only need v 2n. Given v n = , v 2n = (0.5889) 2. Thus P X = (1 (0.5889) 2 ) = Solution: D Equate net present values: v+ 4000v = v xv x 2000 = x = Solution: E 2 2 For the amortization method, payment P is determined by = X X = a, which yields (using calculator) For the sinking fund method, interest is.08 (2000) = 1600 and total payment is given as X, the same as for the amortization method. Thus the sinking fund deposit = X 1600 = = The sinking fund, at rate j, must accumulate to in 20 years. Thus, s 20 j = which yields (using calculator) j = /03/04 13

73 EXAM 2/FM SAMPLE QUESTIONS SOLUTIONS 25. Solution: D The present value of the perpetuity = X/i. Thus, the given information yields: X B= X a = 0.4 n i n C = v Xa n 2n X J = v i 0.4 n a = v = 0.6 n i X J = 0.36 i That is, Jeff s share is 36% of the perpetuity s present value Solution: D The given information yields the following amounts of interest paid: Seth = = = Janice = = ( )( ) 5000 Lori = P(10) 5000 = where P= = a 10 6% The sum is Solution: E X = Bruce s interest is i times the accumulated value at the end of 10 years = i 100 (1+i) 10. X = Robbie s interest is i times the accumulated value at the end of 16 years = i 50 (1+i) 16 Because both amounts equal X, taking the ratio yields: X/X = 2 v 6 or v 6 = 1/2. Thus, (1+i) 6 = 2 and i = 2 1/6 1 = So X = [100 ( ) 10 ]= Solution: D Year (t + 1) principal repaid = v n t Year t interest repaid = i an + = 1 v n t+1 t 1 Total = 1 v n t+1 + v n t = 1 v n t (v 1) = 1 v n t ( (1 v)) = 1 + v n t (d) /03/04 14

74 EXAM 2/FM SAMPLE QUESTIONS SOLUTIONS 29. Solution: B 32 is given as PV of perpetuity paying 10 at end of each 3-year period, with first payment at the end of 3 years. Thus, 32 = 10 (v 3 + v 6 +,,,,,,, ) = 10 v 3 (1/1- v 3 ) (infinite geometric progression), and v 3 = 32/42 or (1+i) 3 = 42/32. Thus, i = X is given as the PV, at the same interest rate, of a perpetuity paying 1 at the end of each 4 months, with the first payment at the end of 4 months. Thus, X = 1 (v 1/3 + v 2/3 +,,,,,,,) = v 1/3 (1/(1- v 1/3 )) = Solution: D The present value of the liability at 5% is \$822, (\$1,000,000/ (1.05^4)). The future value of the bond, including coupons reinvested at 5%, is \$1,000,000. If interest rates drop by ½%, the coupons will be reinvested at an interest rate 4.5%. Annual coupon payments = 822,703 x.05 = 41,135. Accumulated value at 12/31/2007 will be 41,135 + [41,135 x (1.045)] + [41,135 x (1.045^2)] + [41,135 x (1.045^3)] + 822,703 = \$998,687. The amount of the liability payment at 12/31/2007 is \$1,000,000, so the shortfall = 998,687 1,000,000 = -1,313 (loss) If interest rates increase, the coupons could be reinvested at an interest rate of 5.5%, leading to an accumulation of more than the \$1,000,000 needed to fund the liability. Accumulated value at 12/31/2007 will be 41,135 + [41,135 x (1.055)] + [41,135 x (1.055^2)] + [41,135 x (1.055^3)] + 822,703 = \$ 1,001,323. The amount of the liability is \$1,000,000, so the surplus or profit = 1,001,323 1,000,000 = +1,323 profit Solution: D. Present value = 5000 (1.07v v v v v 20 ) 20 1 (1.07v) = v ( ) 1 (1.07v) simplifying to: 5,000 (1.07) [ 1-(1.07/1.05) 20 ] / ( ) = 122, /03/04 15

75 EXAM 2/FM SAMPLE QUESTIONS SOLUTIONS 32. Solution: C. NPV = (1.05) -4 (60000(1.04) ) = (1.05) -4 (122400) = Time Cash Flow Initial Investment Investment Returns Reinvestment Returns Total amount to be discounted -100,000 60,000 60,000 60,000*.04 = , = Discount Factor 1 1/(1.05)^4 = , , Solution: B. Using spot rates, the value of the bond is: 60/(1.07) + 60/((1.08) 2 ) /((1.09) 3 ) = Solution: E. Using spot rates, the value of the bond is: 60/(1.07) + 60/((1.08) 2 ) /((1.09) 3 ) = Thus, the annual effective yield rate, i, for the bond is such that = 60a v at i. This can be 3 easily calculated using one of the calculators allowed on the actuarial exam. For example, using the BA II PLUS the keystrokes are: 3 N, PV, 60 +/- PMT, /- FV, CPT I/Y = and the result is 8.9% (rounded to one decimal place) /03/04 16

76 EXAM 2/FM SAMPLE QUESTIONS SOLUTIONS 35. Solution: C. Duration is defined as n t= 1 n t= 1 tv v t t R R t t, where v is calculated at 8% in this problem. (Note: There is a minor but important error on page 228 of the second edition of Broverman s text. The reference "The quantity in brackets in Equation (4.11) is called the duration of the investment or cash flow" is not correct because of the minus sign in the brackets. There is an errata list for the second edition. Check if you do not have a copy). n The current price of the bond is v t Rt, the denominator of the duration expression, and is given as 100. The t= 1 derivative of price with respect to the yield to maturity is n tv t= 1 t+ 1 R t = - v times the numerator of the duration expression. Thus, the numerator of the duration expression is - (1.08) times the derivative. But the derivative is given as So the numerator of the duration expression is 756. Thus, the duration = 756/100 = Solution: C Duration is defined as t= 1 t= 1 dividend amount. Thus, the duration = tv v t t R R t t, where for this problem v is calculated at i = 10% and R t is a constant D, the t= 1 t= 1 tv v t t D D = t= 1 t= 1 tv v t t. Using the mathematics of infinite geometric progressions (or just remembering the present value for a 1 unit perpetuity immediate), the denominator = v (1/(1-v)) (first term times 1 divided by the quantity 1 minus the common ratio; converges as long as the absolute value of the common ratio, v in this case, is less than 1). This simplifies to 1/i because 1- v = d = i v. The numerator may be remembered as the present value of an increasing perpetuity immediate beginning at unit and increasing by I unit each payment period, which equals 2 i + i = 1+ i 2. So duration = i S Num /denominator =((1+i)/i 2 )/(1/i) = (1+i)/i = 1.1/.1 = /03/04 17

77 EXAM 2/FM SAMPLE QUESTIONS SOLUTIONS 37. Solution: B Duration is defined as t= 1 t= 1 amount, times (1.02) t-1. Thus, the duration = tv v t t R R t t, where for this problem v is calculated at i = 5% and R t is D, the initial dividend t= 1 t= 1 t tv D(1.02) t v D(1.02) t 1 t 1 = t= 1 t= 1 tv v t t (1.02) (1.02) Using the mathematics of infinite geometric progressions (or just remembering the present value for a 1 unit 1 1 geometrically increasing perpetuity immediate), the denominator = v, which simplifies to. It (1 v(1.02)) i i can be shown* that the numerator simplifies to. So duration = numerator/denominator 2 ( i.02) 1+ i 1 1+ i = / =. 2 ( i.02) i.02 i.02 Thus, for i =.05, duration = (1.05)/.03 = 35. Alternative solution: A shorter alternative solution uses the fact that the definition of duration can be can be shown to be equivalent to (1+i) P (i)/p(i) where P(i) = v t Rt. Thus, in this case P(i) = t t 1 D v (1.02) = D 1 t=1 t= 1 i.02 and 1 D( ) 2 1 P (i) (the derivative of P(i) with respect to i) = D ( ) 2 ( i.02). Thus, the duration = ( i.02) (1 + i ) = 1 D i i, yielding the same result as above. i *Note: The process for obtaining the value for the numerator using the mathematics of series simplification is: Let S Num denote the sum in the numerator. Then S Num = 1 v + 2 (1.02) v (1.02) 2 v n (1.02) n-1 v n +.. and (1.02)v S Num = 1 (1.02)v (1.02) 2 v (n-1) (1.02) n-1 v n +.. Thus, (1-(1.02)v) S Num = 1 v + 1 (1.02)v (1.02) 2 v (1.02) n-1 v n +..= i i i and S Num = /(1 (1.02) v) = / = / =. 2 ( i.02) i i i i ( i.02) t 1 t 1. 1 v = (1 v(1.02)) 1 ( i.02) 11/03/04 18

78 EXAM 2/FM SAMPLE QUESTIONS SOLUTIONS /03/04 19

79 EXAM 2/FM SAMPLE QUESTIONS SOLUTIONS 38. Solution: B. Eric s equation of value at end of year: (Value of contributions) 400 (1+i) X + 16 = 800 * (1.08) (Value of returns) (*Proceeds received for stock sale at beginning of year are in non-interest bearing account per government regulations (Kellison top of page 281)) Thus, Eric s yield i = (16 + 2X)/400. Jason s equation of value at end of year: (Value of contributions) 400 (1+j) X + 16 = 800 * (1.08) (Value of returns) Thus, Jason s yield j = (16 X)/400. It is given that Eric s yield i = twice Jason s yield j. So (16 + 2X)/400 = 2 ((16 X)/400), or X = 4. Thus, Eric s yield i = (16 + 8)/400 =.06 or 6% Solution: B. Chris equation of value at end of year: (Value of contributions).5 P(1+i) = P * +.5 P (1.06) (Value of returns), where P = price stock sold for (*Proceeds received for stock sale at beginning of year are in non-interest bearing account per government regulations (Kellison top of page 281)) Thus, Chris yield i = ((1.03) P 760)/(.5 P). Jose s equation of value at end of year: (Value of contributions).5 P(1+j) = P * +.5 P (1.06) (Value of returns), Thus, Jose s yield j = ((1.03) P - 792)/(.5 P). It is given that Chris yield i = twice Jose s yield j. So ((1.03) P 760)/(.5 P) = 2 ((1.03) P - 792)/(.5 P) or P = 824/(1.03) = 800. Thus, Chris yield i = ((1.03) )/400 = 64/400 =.16 or 16% Solution: E. Bill s equation of value at end of year: (Value of contributions) 500 (1+i) + P + X = 1000 * (1.06) (Value of returns) (*Proceeds received for stock sale at beginning of year are in non-interest bearing account per government regulations (Kellison top of page 281)) Thus, Bill s yield i = (1030 P - X)/500. Jane s equation of value at end of year: (Value of contributions) 500 (1+j) + P X = 1000 * (1.06) (Value of returns), Thus, Jane s yield j = (1055 P 2X)/500. It is given that Bill s yield i = Jane s yield j =.21. So (1030 P - X)/500 = (1055 P 2X)/500 or X = 25 and.21 = (1030 P 25)/500 (from Bill s yield), which implies P = (500) = = /03/04 20

### SOCIETY OF ACTUARIES FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS

SOCIETY OF ACTUARIES EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS This page indicates changes made to Study Note FM-09-05. April 28, 2014: Question and solutions 61 were added. January 14, 2014:

### SOCIETY OF ACTUARIES FINANCIAL MATHEMATICS. EXAM FM SAMPLE QUESTIONS Interest Theory

SOCIETY OF ACTUARIES EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS Interest Theory This page indicates changes made to Study Note FM-09-05. January 14, 2014: Questions and solutions 58 60 were

### Study Questions for Actuarial Exam 2/FM By: Aaron Hardiek June 2010

P a g e 1 Study Questions for Actuarial Exam 2/FM By: Aaron Hardiek June 2010 P a g e 2 Background The purpose of my senior project is to prepare myself, as well as other students who may read my senior

### n(n + 1) 2 1 + 2 + + n = 1 r (iii) infinite geometric series: if r < 1 then 1 + 2r + 3r 2 1 e x = 1 + x + x2 3! + for x < 1 ln(1 + x) = x x2 2 + x3 3

ACTS 4308 FORMULA SUMMARY Section 1: Calculus review and effective rates of interest and discount 1 Some useful finite and infinite series: (i) sum of the first n positive integers: (ii) finite geometric

### A) 1.8% B) 1.9% C) 2.0% D) 2.1% E) 2.2%

1 Exam FM Questions Practice Exam 1 1. Consider the following yield curve: Year Spot Rate 1 5.5% 2 5.0% 3 5.0% 4 4.5% 5 4.0% Find the four year forward rate. A) 1.8% B) 1.9% C) 2.0% D) 2.1% E) 2.2% 2.

### 1. Which of the following statements is an implication of the semi-strong form of the. Prices slowly adjust over time to incorporate past information.

COURSE 2 MAY 2001 1. Which of the following statements is an implication of the semi-strong form of the Efficient Market Hypothesis? (A) (B) (C) (D) (E) Market price reflects all information. Prices slowly

### Time Value of Money. 2014 Level I Quantitative Methods. IFT Notes for the CFA exam

Time Value of Money 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction...2 2. Interest Rates: Interpretation...2 3. The Future Value of a Single Cash Flow...4 4. The

### 3. Time value of money. We will review some tools for discounting cash flows.

1 3. Time value of money We will review some tools for discounting cash flows. Simple interest 2 With simple interest, the amount earned each period is always the same: i = rp o where i = interest earned

### LO.a: Interpret interest rates as required rates of return, discount rates, or opportunity costs.

LO.a: Interpret interest rates as required rates of return, discount rates, or opportunity costs. 1. The minimum rate of return that an investor must receive in order to invest in a project is most likely

### substantially more powerful. The internal rate of return feature is one of the most useful of the additions. Using the TI BA II Plus

for Actuarial Finance Calculations Introduction. This manual is being written to help actuarial students become more efficient problem solvers for the Part II examination of the Casualty Actuarial Society

### FinQuiz Notes 2 0 1 5

Reading 5 The Time Value of Money Money has a time value because a unit of money received today is worth more than a unit of money to be received tomorrow. Interest rates can be interpreted in three ways.

### Introduction to Real Estate Investment Appraisal

Introduction to Real Estate Investment Appraisal Maths of Finance Present and Future Values Pat McAllister INVESTMENT APPRAISAL: INTEREST Interest is a reward or rent paid to a lender or investor who has

### Finance CHAPTER OUTLINE. 5.1 Interest 5.2 Compound Interest 5.3 Annuities; Sinking Funds 5.4 Present Value of an Annuity; Amortization

CHAPTER 5 Finance OUTLINE Even though you re in college now, at some time, probably not too far in the future, you will be thinking of buying a house. And, unless you ve won the lottery, you will need

### Lecture Notes on the Mathematics of Finance

Lecture Notes on the Mathematics of Finance Jerry Alan Veeh February 20, 2006 Copyright 2006 Jerry Alan Veeh. All rights reserved. 0. Introduction The objective of these notes is to present the basic aspects

### Financial Mathematics Exam

2014 Exam 2 Syllabus Financial Mathematics Exam The purpose of the syllabus for this examination is to develop knowledge of the fundamental concepts of financial mathematics and how those concepts are

### 2015 Exam 2 Syllabus Financial Mathematics Exam

2015 Exam 2 Syllabus Financial Mathematics Exam The syllabus for this exam is defined in the form of learning objectives that set forth, usually in broad terms, what the candidate should be able to do

### Compound Interest. Invest 500 that earns 10% interest each year for 3 years, where each interest payment is reinvested at the same rate:

Compound Interest Invest 500 that earns 10% interest each year for 3 years, where each interest payment is reinvested at the same rate: Table 1 Development of Nominal Payments and the Terminal Value, S.

### CHAPTER 8 INTEREST RATES AND BOND VALUATION

CHAPTER 8 INTEREST RATES AND BOND VALUATION Solutions to Questions and Problems 1. The price of a pure discount (zero coupon) bond is the present value of the par value. Remember, even though there are

### Course FM / Exam 2. Calculator advice

Course FM / Exam 2 Introduction It wasn t very long ago that the square root key was the most advanced function of the only calculator approved by the SOA/CAS for use during an actuarial exam. Now students

### INSTITUTE AND FACULTY OF ACTUARIES EXAMINATION

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 INSTITUTE AND FACULTY OF ACTUARIES EXAMINATION 12 April 2016 (am) Subject CT1 Financial Mathematics Core

### INSTITUTE OF ACTUARIES OF INDIA

INSTITUTE OF ACTUARIES OF INDIA EXAMINATIONS 15 th November 2010 Subject CT1 Financial Mathematics Time allowed: Three Hours (15.00 18.00 Hrs) Total Marks: 100 INSTRUCTIONS TO THE CANDIDATES 1. Please

### Discounted Cash Flow Valuation

6 Formulas Discounted Cash Flow Valuation McGraw-Hill/Irwin Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter Outline Future and Present Values of Multiple Cash Flows Valuing

### APPENDIX. Interest Concepts of Future and Present Value. Concept of Interest TIME VALUE OF MONEY BASIC INTEREST CONCEPTS

CHAPTER 8 Current Monetary Balances 395 APPENDIX Interest Concepts of Future and Present Value TIME VALUE OF MONEY In general business terms, interest is defined as the cost of using money over time. Economists

### Certified Actuarial Analyst Resource Guide Module 1

Certified Actuarial Analyst Resource Guide Module 1 2014/2015 November 2014 Disclaimer: This Module 1 Resource Guide has been prepared by and/or on behalf of the Institute and Faculty of Actuaries (IFoA).

### Lecture Notes on Actuarial Mathematics

Lecture Notes on Actuarial Mathematics Jerry Alan Veeh May 1, 2006 Copyright 2006 Jerry Alan Veeh. All rights reserved. 0. Introduction The objective of these notes is to present the basic aspects of the

### Time Value of Money. Reading 5. IFT Notes for the 2015 Level 1 CFA exam

Time Value of Money Reading 5 IFT Notes for the 2015 Level 1 CFA exam Contents 1. Introduction... 2 2. Interest Rates: Interpretation... 2 3. The Future Value of a Single Cash Flow... 4 4. The Future Value

### Time-Value-of-Money and Amortization Worksheets

2 Time-Value-of-Money and Amortization Worksheets The Time-Value-of-Money and Amortization worksheets are useful in applications where the cash flows are equal, evenly spaced, and either all inflows or

### The Time Value of Money

The following is a review of the Quantitative Methods: Basic Concepts principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in: The Time

### 380.760: Corporate Finance. Financial Decision Making

380.760: Corporate Finance Lecture 2: Time Value of Money and Net Present Value Gordon Bodnar, 2009 Professor Gordon Bodnar 2009 Financial Decision Making Finance decision making is about evaluating costs

### CARMEN VENTER COPYRIGHT www.futurefinance.co.za 0828807192 1

Carmen Venter CFP WORKSHOPS FINANCIAL CALCULATIONS presented by Geoff Brittain Q 5.3.1 Calculate the capital required at retirement to meet Makhensa s retirement goals. (5) 5.3.2 Calculate the capital

### CHAPTER 7: FIXED-INCOME SECURITIES: PRICING AND TRADING

CHAPTER 7: FIXED-INCOME SECURITIES: PRICING AND TRADING Topic One: Bond Pricing Principles 1. Present Value. A. The present-value calculation is used to estimate how much an investor should pay for a bond;

### ICASL - Business School Programme

ICASL - Business School Programme Quantitative Techniques for Business (Module 3) Financial Mathematics TUTORIAL 2A This chapter deals with problems related to investing money or capital in a business

### Vilnius University. Faculty of Mathematics and Informatics. Gintautas Bareikis

Vilnius University Faculty of Mathematics and Informatics Gintautas Bareikis CONTENT Chapter 1. SIMPLE AND COMPOUND INTEREST 1.1 Simple interest......................................................................

### Annuity is defined as a sequence of n periodical payments, where n can be either finite or infinite.

1 Annuity Annuity is defined as a sequence of n periodical payments, where n can be either finite or infinite. In order to evaluate an annuity or compare annuities, we need to calculate their present value

### THE TIME VALUE OF MONEY

QUANTITATIVE METHODS THE TIME VALUE OF MONEY Reading 5 http://proschool.imsindia.com/ 1 Learning Objective Statements (LOS) a. Interest Rates as Required rate of return, Discount Rate and Opportunity Cost

### Dick Schwanke Finite Math 111 Harford Community College Fall 2013

Annuities and Amortization Finite Mathematics 111 Dick Schwanke Session #3 1 In the Previous Two Sessions Calculating Simple Interest Finding the Amount Owed Computing Discounted Loans Quick Review of

### Chapter 04 - More General Annuities

Chapter 04 - More General Annuities 4-1 Section 4.3 - Annuities Payable Less Frequently Than Interest Conversion Payment 0 1 0 1.. k.. 2k... n Time k = interest conversion periods before each payment n

### Time Value of Money. 2014 Level I Quantitative Methods. IFT Notes for the CFA exam

Time Value of Money 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction... 2 2. Interest Rates: Interpretation... 2 3. The Future Value of a Single Cash Flow... 4 4. The

### Time Value of Money 1

Time Value of Money 1 This topic introduces you to the analysis of trade-offs over time. Financial decisions involve costs and benefits that are spread over time. Financial decision makers in households

### Manual for SOA Exam FM/CAS Exam 2.

Manual for SOA Exam FM/CAS Exam 2. Chapter 5. Bonds. c 2009. Miguel A. Arcones. All rights reserved. Extract from: Arcones Manual for the SOA Exam FM/CAS Exam 2, Financial Mathematics. Fall 2009 Edition,

### Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Chapter Outline. Multiple Cash Flows Example 2 Continued

6 Calculators Discounted Cash Flow Valuation Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute

### Review Solutions FV = 4000*(1+.08/4) 5 = \$4416.32

Review Solutions 1. Planning to use the money to finish your last year in school, you deposit \$4,000 into a savings account with a quoted annual interest rate (APR) of 8% and quarterly compounding. Fifteen

### Problem Set: Annuities and Perpetuities (Solutions Below)

Problem Set: Annuities and Perpetuities (Solutions Below) 1. If you plan to save \$300 annually for 10 years and the discount rate is 15%, what is the future value? 2. If you want to buy a boat in 6 years

### 300 Chapter 5 Finance

300 Chapter 5 Finance 17. House Mortgage A couple wish to purchase a house for \$200,000 with a down payment of \$40,000. They can amortize the balance either at 8% for 20 years or at 9% for 25 years. Which

### 5.1 Simple and Compound Interest

5.1 Simple and Compound Interest Question 1: What is simple interest? Question 2: What is compound interest? Question 3: What is an effective interest rate? Question 4: What is continuous compound interest?

### Chapter 6 Contents. Principles Used in Chapter 6 Principle 1: Money Has a Time Value.

Chapter 6 The Time Value of Money: Annuities and Other Topics Chapter 6 Contents Learning Objectives 1. Distinguish between an ordinary annuity and an annuity due, and calculate present and future values

### Dick Schwanke Finite Math 111 Harford Community College Fall 2013

Annuities and Amortization Finite Mathematics 111 Dick Schwanke Session #3 1 In the Previous Two Sessions Calculating Simple Interest Finding the Amount Owed Computing Discounted Loans Quick Review of

### Chapter 6. Discounted Cash Flow Valuation. Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Answer 6.1

Chapter 6 Key Concepts and Skills Be able to compute: the future value of multiple cash flows the present value of multiple cash flows the future and present value of annuities Discounted Cash Flow Valuation

### Time Value of Money Practice Questions Irfanullah.co

1. You are trying to estimate the required rate of return for a particular investment. Which of the following premiums are you least likely to consider? A. Inflation premium B. Maturity premium C. Nominal

### 1 Cash-flows, discounting, interest rate models

Assignment 1 BS4a Actuarial Science Oxford MT 2014 1 1 Cash-flows, discounting, interest rate models Please hand in your answers to questions 3, 4, 5 and 8 for marking. The rest are for further practice.

### Compound Interest Formula

Mathematics of Finance Interest is the rental fee charged by a lender to a business or individual for the use of money. charged is determined by Principle, rate and time Interest Formula I = Prt \$100 At

### Chapter 6. Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams

Chapter 6 Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams 1. Distinguish between an ordinary annuity and an annuity due, and calculate present

### Mathematics. Rosella Castellano. Rome, University of Tor Vergata

and Loans Mathematics Rome, University of Tor Vergata and Loans Future Value for Simple Interest Present Value for Simple Interest You deposit E. 1,000, called the principal or present value, into a savings

### The Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820)

The Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820) Using the Sharp EL-738 Calculator Reference is made to the Appendix Tables A-1 to A-4 in the course textbook Investments:

### Section 8.1. I. Percent per hundred

1 Section 8.1 I. Percent per hundred a. Fractions to Percents: 1. Write the fraction as an improper fraction 2. Divide the numerator by the denominator 3. Multiply by 100 (Move the decimal two times Right)

### Nominal rates of interest and discount

1 Nominal rates of interest and discount i (m) : The nominal rate of interest payable m times per period, where m is a positive integer > 1. By a nominal rate of interest i (m), we mean a rate payable

### 2016 Wiley. Study Session 2: Quantitative Methods Basic Concepts

2016 Wiley Study Session 2: Quantitative Methods Basic Concepts Reading 5: The Time Value of Money LESSO 1: ITRODUCTIO, ITEREST RATES, FUTURE VALUE, AD PREST VALUE The Financial Calculator It is very important

### Solutions to Supplementary Questions for HP Chapter 5 and Sections 1 and 2 of the Supplementary Material. i = 0.75 1 for six months.

Solutions to Supplementary Questions for HP Chapter 5 and Sections 1 and 2 of the Supplementary Material 1. a) Let P be the recommended retail price of the toy. Then the retailer may purchase the toy at

### Finding the Payment \$20,000 = C[1 1 / 1.0066667 48 ] /.0066667 C = \$488.26

Quick Quiz: Part 2 You know the payment amount for a loan and you want to know how much was borrowed. Do you compute a present value or a future value? You want to receive \$5,000 per month in retirement.

### Fixed Income: Practice Problems with Solutions

Fixed Income: Practice Problems with Solutions Directions: Unless otherwise stated, assume semi-annual payment on bonds.. A 6.0 percent bond matures in exactly 8 years and has a par value of 000 dollars.

### ST334 ACTUARIAL METHODS

ST334 ACTUARIAL METHODS version 214/3 These notes are for ST334 Actuarial Methods. The course covers Actuarial CT1 and some related financial topics. Actuarial CT1 which is called Financial Mathematics

### Management Accounting Financial Strategy

PAPER P9 Management Accounting Financial Strategy The Examiner provides a short study guide, for all candidates revising for this paper, to some first principles of finance and financial management Based

### Exam 1 Morning Session

91. A high yield bond fund states that through active management, the fund s return has outperformed an index of Treasury securities by 4% on average over the past five years. As a performance benchmark

### CHAPTER 4. Definition 4.1 Bond A bond is an interest-bearing certificate of public (government) or private (corporate) indebtedness.

CHAPTER 4 BOND VALUATION Gentlemen prefer bonds. Andrew Mellon, 1855-1937 It is often necessary for corporations and governments to raise funds to cover planned expenditures. Corporations have two main

### Time Value of Money. Work book Section I True, False type questions. State whether the following statements are true (T) or False (F)

Time Value of Money Work book Section I True, False type questions State whether the following statements are true (T) or False (F) 1.1 Money has time value because you forgo something certain today for

### FinQuiz Notes 2 0 1 4

Reading 5 The Time Value of Money Money has a time value because a unit of money received today is worth more than a unit of money to be received tomorrow. Interest rates can be interpreted in three ways.

### Chapter 03 - Basic Annuities

3-1 Chapter 03 - Basic Annuities Section 7.0 - Sum of a Geometric Sequence The form for the sum of a geometric sequence is: Sum(n) a + ar + ar 2 + ar 3 + + ar n 1 Here a = (the first term) n = (the number

### CALCULATOR TUTORIAL. Because most students that use Understanding Healthcare Financial Management will be conducting time

CALCULATOR TUTORIAL INTRODUCTION Because most students that use Understanding Healthcare Financial Management will be conducting time value analyses on spreadsheets, most of the text discussion focuses

### The Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820)

The Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820) Using the Sharp EL-733A Calculator Reference is made to the Appendix Tables A-1 to A-4 in the course textbook Investments:

### Introduction to the Hewlett-Packard (HP) 10BII Calculator and Review of Mortgage Finance Calculations

Introduction to the Hewlett-Packard (HP) 10BII Calculator and Review of Mortgage Finance Calculations Real Estate Division Sauder School of Business University of British Columbia Introduction to the Hewlett-Packard

### The Institute of Chartered Accountants of India

CHAPTER 4 SIMPLE AND COMPOUND INTEREST INCLUDING ANNUITY APPLICATIONS SIMPLE AND COMPOUND INTEREST INCLUDING ANNUITY- APPLICATIONS LEARNING OBJECTIVES After studying this chapter students will be able

### 14 ARITHMETIC OF FINANCE

4 ARITHMETI OF FINANE Introduction Definitions Present Value of a Future Amount Perpetuity - Growing Perpetuity Annuities ompounding Agreement ontinuous ompounding - Lump Sum - Annuity ompounding Magic?

### Chapter 5 Time Value of Money 2: Analyzing Annuity Cash Flows

1. Future Value of Multiple Cash Flows 2. Future Value of an Annuity 3. Present Value of an Annuity 4. Perpetuities 5. Other Compounding Periods 6. Effective Annual Rates (EAR) 7. Amortized Loans Chapter

### Chapter 9 Bonds and Their Valuation ANSWERS TO SELECTED END-OF-CHAPTER QUESTIONS

Chapter 9 Bonds and Their Valuation ANSWERS TO SELECTED END-OF-CHAPTER QUESTIONS 9-1 a. A bond is a promissory note issued by a business or a governmental unit. Treasury bonds, sometimes referred to as

### Chapter Two. THE TIME VALUE OF MONEY Conventions & Definitions

Chapter Two THE TIME VALUE OF MONEY Conventions & Definitions Introduction Now, we are going to learn one of the most important topics in finance, that is, the time value of money. Note that almost every

### 2. Determine the appropriate discount rate based on the risk of the security

Fixed Income Instruments III Intro to the Valuation of Debt Securities LOS 64.a Explain the steps in the bond valuation process 1. Estimate the cash flows coupons and return of principal 2. Determine the

### ANALYSIS OF FIXED INCOME SECURITIES

ANALYSIS OF FIXED INCOME SECURITIES Valuation of Fixed Income Securities Page 1 VALUATION Valuation is the process of determining the fair value of a financial asset. The fair value of an asset is its

### 5. Time value of money

1 Simple interest 2 5. Time value of money With simple interest, the amount earned each period is always the same: i = rp o We will review some tools for discounting cash flows. where i = interest earned

### The Basics of Interest Theory

Contents Preface 3 The Basics of Interest Theory 9 1 The Meaning of Interest................................... 10 2 Accumulation and Amount Functions............................ 14 3 Effective Interest

### Discounted Cash Flow Valuation

Discounted Cash Flow Valuation Chapter 5 Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute

### REVIEW MATERIALS FOR REAL ESTATE ANALYSIS

REVIEW MATERIALS FOR REAL ESTATE ANALYSIS 1997, Roy T. Black REAE 5311, Fall 2005 University of Texas at Arlington J. Andrew Hansz, Ph.D., CFA CONTENTS ITEM ANNUAL COMPOUND INTEREST TABLES AT 10% MATERIALS

### Module 5: Interest concepts of future and present value

Page 1 of 23 Module 5: Interest concepts of future and present value Overview In this module, you learn about the fundamental concepts of interest and present and future values, as well as ordinary annuities

### VALUE 11.125%. \$100,000 2003 (=MATURITY

NOTES H IX. How to Read Financial Bond Pages Understanding of the previously discussed interest rate measures will permit you to make sense out of the tables found in the financial sections of newspapers

### Chapter 2. CASH FLOW Objectives: To calculate the values of cash flows using the standard methods.. To evaluate alternatives and make reasonable

Chapter 2 CASH FLOW Objectives: To calculate the values of cash flows using the standard methods To evaluate alternatives and make reasonable suggestions To simulate mathematical and real content situations

### CHAPTER 6. Accounting and the Time Value of Money. 2. Use of tables. 13, 14 8 1. a. Unknown future amount. 7, 19 1, 5, 13 2, 3, 4, 6

CHAPTER 6 Accounting and the Time Value of Money ASSIGNMENT CLASSIFICATION TABLE (BY TOPIC) Topics Questions Brief Exercises Exercises Problems 1. Present value concepts. 1, 2, 3, 4, 5, 9, 17, 19 2. Use

### Future Value of an Annuity Sinking Fund. MATH 1003 Calculus and Linear Algebra (Lecture 3)

MATH 1003 Calculus and Linear Algebra (Lecture 3) Future Value of an Annuity Definition An annuity is a sequence of equal periodic payments. We call it an ordinary annuity if the payments are made at the

### You just paid \$350,000 for a policy that will pay you and your heirs \$12,000 a year forever. What rate of return are you earning on this policy?

1 You estimate that you will have \$24,500 in student loans by the time you graduate. The interest rate is 6.5%. If you want to have this debt paid in full within five years, how much must you pay each

### Matt 109 Business Mathematics Notes. Spring 2013

1 To be used with: Title: Business Math (Without MyMathLab) Edition: 8 th Author: Cleaves and Hobbs Publisher: Pearson/Prentice Hall Copyright: 2009 ISBN #: 978-0-13-513687-4 Matt 109 Business Mathematics

### 1. If you wish to accumulate \$140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%?

Chapter 2 - Sample Problems 1. If you wish to accumulate \$140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%? 2. What will \$247,000 grow to be in

### PRESENT VALUE ANALYSIS. Time value of money equal dollar amounts have different values at different points in time.

PRESENT VALUE ANALYSIS Time value of money equal dollar amounts have different values at different points in time. Present value analysis tool to convert CFs at different points in time to comparable values

### \$496. 80. Example If you can earn 6% interest, what lump sum must be deposited now so that its value will be \$3500 after 9 months?

Simple Interest, Compound Interest, and Effective Yield Simple Interest The formula that gives the amount of simple interest (also known as add-on interest) owed on a Principal P (also known as present

### Chapter 1: Time Value of Money

1 Chapter 1: Time Value of Money Study Unit 1: Time Value of Money Concepts Basic Concepts Cash Flows A cash flow has 2 components: 1. The receipt or payment of money: This differs from the accounting

### Time Value of Money Problems

Time Value of Money Problems 1. What will a deposit of \$4,500 at 10% compounded semiannually be worth if left in the bank for six years? a. \$8,020.22 b. \$7,959.55 c. \$8,081.55 d. \$8,181.55 2. What will

### CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES

Chapter - The Term Structure of Interest Rates CHAPTER : THE TERM STRUCTURE OF INTEREST RATES PROBLEM SETS.. In general, the forward rate can be viewed as the sum of the market s expectation of the future

### Real Estate. Refinancing

Introduction This Solutions Handbook has been designed to supplement the HP-2C Owner's Handbook by providing a variety of applications in the financial area. Programs and/or step-by-step keystroke procedures

1.0 ALTERNATIVE SOURCES OF FINANCE Module 1: Corporate Finance and the Role of Venture Capital Financing Alternative Sources of Finance TABLE OF CONTENTS 1.1 Short-Term Debt (Short-Term Loans, Line of

### US TREASURY SECURITIES - Issued by the U.S. Treasury Department and guaranteed by the full faith and credit of the United States Government.

Member NASD/SIPC Bond Basics TYPES OF ISSUERS There are essentially five entities that issue bonds: US TREASURY SECURITIES - Issued by the U.S. Treasury Department and guaranteed by the full faith and